You can restore hard plastics, such as acrylic and polycarbonate, by sanding them, and the procedure is similar to sanding a wood finish. Because plastic scratches easily, coarse sandpaper grits aren't recommended. The best strategy is to begin wet sanding with 220-grit sandpaper and make additional passes with progressively finer paper until you're happy with the appearance.
Wet Sanding Technique
The type of sandpaper you need for wet sanding is called silicon carbide -- or wet/dry -- sandpaper. It's usually black or gray. Immerse the paper in water for 10 minutes, then sand in a circular motion. Keep the sanding pattern irregular to avoid producing deep scratches that might remain visible. Using a foam block to support the sandpaper is helpful when sanding curved surfaces, such as headlight lenses.
A Typical Procedure
Before sanding, clean off dirt and grime with a mild detergent solution. Use a 50/50 solution of vinegar and water to clean extensively pitted plastic, because vinegar is a weak acid, and it helps smooth the surface. Run through the sanding grits in order from 220- to 400-, 800- and 1,200-grit, finishing with 1,500- or 2,000-grit, depending on how smooth you want the surface. Clean sanding residue with water after you're done with each grit. To get the maximum sheen, spread automotive clear-coat polishing compound on the surface and buff it with a lambswool buffer.